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This paper presents a formation control method to solve the moving target tracking problem for a swarm of unmanned aerial vehicles (UAVs). The formation is achieved by the artificial potential field with both attractive and repulsive forces, and each UAV in the swarm will be driven into a leader-centered spherical surface. The leader is controlled by the attractive force by the moving target, while the Lyapunov vectors drive the leader UAV to a fly-around circle of the target. Furthermore, the rotational vector-based potential field is applied to achieve the obstacle avoidance of UAVs with smooth trajectories and avoid the local optima problem. The efficiency of the developed control scheme is verified by numerical simulations in four scenarios.

The convective instability of the natural convection boundary layers of air (Pr = 0.7) in the laminar-to-turbulent transition regime (Ra = 8.7 × 10 7 -1.1 × 10 9 ) is investigated by stability analysis in the framework of direct numerical simulations. To understand the spatial and temporal evolution of the convective instability of the thermal boundary layers, small-amplitude random-mode numerical perturbations are first introduced into the boundary condition of the boundary layer flow. The prescribed full spectral perturbations (i.e., white noise) are mostly damped out immediately by a limited upstream boundary layer. A low-frequency band is initially distinct in the upstream near the leading edge but decays spatially as the instability propagates downstream. In contrast, a high-frequency band emerges to finally become the most dominant frequency band in the thermal boundary layer transition regime. To obtain further insights into the nature of the established high-frequency band, single-mode perturbations of various frequencies are then introduced into the boundary layer near the leading edge. It is found that a single-mode perturbation at the peak frequency within the high-frequency band excites the maximum response of the thermal boundary layer, suggesting that the peak frequency is in fact the characteristic frequency or resonance frequency of the thermal boundary layer. The dimensionless form of the dependence of the characteristic frequency on Ra is then found to be fc = 0.07Ra 2/3 . The single-mode perturbation numerical experiments also revealed the propagation speed of convective instability waves, which was significantly greater than the convection speed of the thermal boundary layer. The smaller the Ra, the larger the difference between the two propagation speeds. A semi-analytical scaling of the wave propagation speed in the form csc ∼ Ra 1/2 y 1/2 Pr was derived (y denoting the streamwise location of the boundary layer), providing a predictive correlation that can be used for thermal boundary layer control.

This study is concerned with structural vibration reduction using a four-parameter isolator designed as a scissor-like structure, which can induce geometric nonlinearity during the deformation process. The displacement transmissibility of the isolator including the geometric nonlinearity under base excitations is thoroughly investigated. First, the dynamic model of the four-parameter isolator is presented. Then, by utilizing the harmonic balanced method (HBM), the steady-state solutions of the inertia mass and auxiliary spring of the proposed isolator are derived. The analytical solutions are validated by comparing with those obtained by the direct numerical integrating method. Besides, the natural frequency of the nonlinear isolation system is presented and investigated. Moreover, the isolation performance of the four-parameter isolator is assessed in terms of the relative and absolute displacement transmissibilities, and compared with that of the linear Zener model, by which the advantages of the present isolator have been clearly revealed. The effects of various design parameters on the displacement transmissibility of the isolator are also analyzed. Finally, a further comparison between the analytical and experimental results under base excitation also shows that the mechanical model used for the four-parameter isolator is accuracy enough. The present results may provide a useful theoretical basis for the design of the four-parameter isolator in engineering practice.

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